Capillary pressure and relative permeability are the most basic rock-fluid properties in multiphase flows. In laboratory, two types of experimental techniques are generally used for determining relative permeability: steady-state and unsteady-state methods. For steady-state methods, the two fluids are injected simultaneously into the porous medium at a fixed ratio until the inflows equal the outflows and a constant pressure drop have been reached. It may take 2 to 40 hours or even longer to reach the steady-state conditions. According to Dullien F., Porous Media: fluid transport and pore structure, 2nd Edition, Academic Press, New York (1991), 139-176 and Bear J., Dynamics of Fluids in Porous Media, Dover Publications, New York, (1972), 444, which is incorporated herein by reference in its entirety, the relative permeability corresponding to the saturation established during the experiment can be determined by a modified form of Darcy's law:
                                                        Q              j                        A                    =          -                ⁣                              K            ⁢                                                  ⁢                          K              rj                                            μ            j                          ⁣                              Δ            ⁢                                                  ⁢                          P              j                                L                                    (        1        )            where Qj, Pj, μj, and Krj are volume flux, pressure, viscosity; and relative permeability of fluid phase j, respectively. A, K, and L are the cross-sectional area, absolute permeability and length of the porous medium, respectively.
The injection ratio is then changed, until a new steady flow is established to calculate the relative permeability corresponding to this saturation. Different approaches may be employed to eliminate the capillary end effects and try to ensure uniform saturation distribution in the whole sample. The steady-state measurements are very time consuming. In addition, the conditions of steady-state and uniform saturation distribution are very rarely reached, and errors are introduced therefrom.
SPRITE MRI
Standard SPRITE MRI
The standard SPRITE MRI technique as taught in Balcom B., J. Barrita, C. Choi, S. Beyea, D. Goodyear and T. Bremner, Single-point magnetic resonance imaging (MRI) of cement based materials, Materials and Structures 36, 166 (2003), which is incorporated herein by reference in its entirety, has proven to be a very robust and flexible method for the study of a wide range of systems with short MR relaxation times. As a pure phase encoding technique, SPRITE is largely immune to image distortions due to susceptibility variation, chemical shift, and paramagnetic impurities. Repetitive excitation and data acquisition are performed in the presence of ramped phase encoding gradients, which enable systems with T2* lifetimes as short as tens of microseconds to be successfully visualized.
Centric Scan SPRITE MRI
A centric scan strategy for SPRITE MRI as taught in Balcom B., R. MacGregor, S. Beyea, D. Green, R. Armstrong and T. Bremner, Single Point Ramped Imaging with T1 Enhancement (SPRITE), J. Magn. Reson. A 123, 131 (1996) and Mastikhin I., B. Balcom, P. Prado and C. Kennedy, SPRITE MRI with Prepared Magnetization and Centric k Space Sampling, J. Magn. Reson. 136, 159 (1999), which are incorporated herein by reference in their entirety, removes the longitudinal steady state from the image intensity equation of standard SPRITE imaging, and increases the inherent image intensity. The image signal intensity no longer depends on the longitudinal relaxation time and the repetition time. These features ensure that centric scan SPRITE is an ideal method for quantitative imaging of sedimentary rocks with short relaxation times.